Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Comparison of Confidence Intervals for the Reliability of the Stress-Strength Models with Explanatory Variables

  • Eun Sik Park (Statistical Research Institute, Seoul National University, Seoul, 151-742, Korea) ;
  • Jae Joo Kim (Professor, Department of Computer Science and Statistics, Seoul National University, Seoul 151-742) ;
  • Sung Hyun Park (Professor, Department of Computer Science and Statistics, Seoul National University, Seoul 151-742)
  • Published : 1996.04.01
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Abstract

In this paper, we consider the distribution-free confidence intervals for the reliability of the stress-strength model when the stress X and strength Y depend linearly on some explanatory variables z and w, respectively. We apply these confidence intervals to the Rocket-Motor data and compare the results to those of Guttman et al. (1988). Some simulation results show that the distribution-free confidence intervals have better performance for nonnormal errors compared to those of Guttman et al. (1988), which are designed for normal random variables in respect that the former yield the coverage levels closer to the nominal coverage level than the latter.

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References

  1. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability v.1 On a use of the Mann-Whitney statistic Birnbaum, Z. W.
  2. Technometrics v.30 Confidence limits for stress-strength models with explanatory variables Guttman, I.;Johnson, R. A.;Bhattacharyya, G. K.;Reiser, B.
  3. Journal of the American Statistical Association v.85 Confidence intervals for probabilities and tolerance regions based on a generalization of the Mann-Whitney statistic Mee, R. W.
  4. Ph.D. thesis, Seoul National University Nonparametric estimation for the reliability of the stress-strength models with explanatory variables Park, E. S.
  5. Sankhya v.A29 A note on asymptotically distribution-free confidence bounds for P(X